In circle A shown below, Segment BD is a diameter and the measure of Arc CB is 48°:
2 answers:
Answer:
66°
Step-by-step explanation:
<em>See attached picture.</em>
<em>When an angle intercepts an arc, </em><em>ARC AC</em><em>, and forms in the </em><em>center [central angle]</em><em>, the angle has </em><em>SAME</em><em> measure as the ARC AC </em><em>[denoted by x]</em><em>. When the angle formed is on the opposite side, it has a measure </em><em>HALF</em><em> of that ARC AC </em><em>[denoted ]</em>
If you look at the problem given, ∠DBC is intercepted by ARC DC and falls in the opposite side of the circle, NOT in the CENTER. <em>Hence </em><em>∠DBC</em><em> has a measure that is </em><em>HALF of ARC DC</em><em>.</em>
<em>There are </em><em>360 degrees in a circle.</em><em> </em><em>ARC DB</em><em> has 2 endpoints that are the diameter of the circle, so </em><em>ARC DB</em><em> has a measure of </em><em>180 degrees</em><em>. </em>Also,
ARC DB = ARC DC + ARC CB
ARC DB = ARC DC + 48
180 = ARC DC + 48
ARC DC = 180 - 48 = 132
Since, ∠DBC = 0.5 * ARC DC, we have:
∠DBC = 0.5 * (132)
∠DBC = 66
Our answer is the second choice of 66°.
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